A certain sequence of numbers called the Narayana numbers and a certain class of polynomials called Narayana polynomials, which were both named after him for his work in bringing out their importance in lattice path theory, have found extensive and varied applications in combinatorics and lattice theory.
He was awarded the PhD degree in mathematical statistics in the year 1954 for a dissertation titled Sequential Procedures in Probit Analysis.
[2] After securing PhD, Narayana did Post-Doctoral work at Indian Council of Agricultural Research, New Delhi and at the Henri Poincare Institute in Paris.
He made seminal contributions to the theory of tournaments, compositions, sampling plans and lattice path combinatorics.
[3] Much of his work was collected together in a monograph titled "Lattice Path Combinatorics with Statistical Applications", published by the University of Toronto Press in 1979.